Sleeping beauty, the doomsday argument and the error of drawing twice.
Suppose there are ten white marbles in an urn. If I draw one of them, what was the probability that I would draw that specific one? If your answer is 1⁄10 you’ve just drawn twice. Once to determine the identity of the marble and once to draw it out of the others. If you only draw once, than “that specific one” simply refers to the marble that you drew making the “probability” 1. You cannot follow the identity back after you drew it, because drawing it was the cause for attributing an identity to it. Identity in this sense is in the map not the territory.
This is the same mistake that sleeping beauty makes. She draws once to determine her own identity and once again to draw out of the other “possibilities”. The same mistake is behind the doomsday argument. You draw once to determine your own identity and once again to draw yourself out of all the humans. There is no 2⁄3 probability that Ogh the neanderthal was one of the last 2⁄3 of all humans. As soon as you say “But I am not Ogh the neanderthal” you are drawing a second time. Otherwise all marbles are white, i.e. all humans are conscious.
You should elaborate more. Probably by working through the Sleeping Beauty problem to see if you can resolve things by sticking “1” in the right places. That would definitely lend support to your ideas.
(this was a decent explanation, you could edit it into your post).
This makes it seem that you could benefit from reading about the difference between de dicto and de re.
That distinction is actually quite important for my argument. If you have 10 white marbles and don’t draw one and I asked you “what is the probability that I will draw this specific marble?” you would ask “What marble?” because there has not yet been any event causing you to identify one of the marbles. Thus you need to make one drawing to make an identification. Before you do that drawing there is no de re because there is not yet a “re”. Once you made that first drawing you have an event that causes an identification. And because this first drawing is what you use to identify the one marble, you cannot use this identification before the drawing. Thus even after the first drawing there is no de re interpretation of questions about states before the drawing like the probability of drawing that marble.
The problem here is the recurring one of how to apply probability in the real world. We have the same model for the situation in which we have an urn, and are about to draw a ball from it, as we do for the situation in which somebody announces that they have just drawn a ball from the same urn, and asks us to speculate on which ball it might have been. We can perhaps agree that if we knew yesterday exactly what procedure was to be carried out today then it is reasonable to use the same model in each case, but there are, as you point out, examples where it’s not obvious which of various possible protocols are being followed.
It might help to set out exactly how you believe “drawing twice” manifests itself in each of your examples.
At −3 Karma I’m not too eager to make that effort. But a bit more details might be helpful.
Let’s take the doomsday argument (the sleeping beauty is a bit more complex). The argument is that there’s a 2⁄3 probability to be one of the last 2⁄3 of humans, therefore doom is immanent (or imminent, I can never remember which is which).
In this argument you are “drawing twice”. The first drawing is the drawing to identify yourself, the second drawing is drawing yourself out of all humans. However, you are in fact only “drawn” once in identifying yourself through your conciousness. There is nobody there to draw you a second time. Therfore the argument is wrong. If we remove the first drawing, leaving only the second one, The probability is of course 2⁄3 that we will draw some human out of the last 2⁄3. But that might be Zzydrh the star explorer, that single drawing will be you only with the probability 1 to the number of humans that will have existed.
If on the other hand we remove the second drawing, leaving only the first, you cannot ask what human you probably are, because we have only drawn once and called that one human “you”, i.e. each and every human to exist draws only himself out of the urn. None is drawn twice and none is not drawn. Imagine a line of humans each drawing one marble. Now ask the first one in line after he has drawn what the probability was that he drew the first marble. If you by any means identify one of the humans as “you”, you have made a second drawing, which in real life doesn’t happen.
I’m hearing words that make me think of the Axiom of Choice. Are you saying that you suspect a formal solution to the sleeping beauty problem has different answers depending on whether or not we have this axiom at our disposal?
If the voting seems honestly not justified, take it as a sign that you’re dealing with too great an inferential distance. If you can’t tell whether the down voting is justified, ask for feedback that contains a URL so you can learn whatever it is that is so obvious to everyone else :-)
I had a similar feeling, but if there are finite examples of the phenomenon, then AC is unlikely to be significant.
As I understand it, in your presentation the doomsday argument corresponds to some of the human-marbles being coloured red, and then asking the first marble in the line what the probability that he was coloured red is: to me the problem appears to be directing questions at samples from probability spaces. I’m now perilously close to just giving a careless analysis of the doomsday argument though.
I think you may have attached the phrase “second drawing” to a useful concept, but it’s not entirely clear what that is. If you can find a lucid explanation, then we might learn something.
There is a 100% chance that I am who I am. There is a 100% chance that I’m Daniel Carrier, given that I’m Daniel Carrier. There is a vanishingly small probability that I’m Daniel Carrier, and a similar probability that I’m Elizer Yudkowsky.
I know that I’m Daniel Carrier, but I can still calculate the probability of it without using as a given. This seems pretty pointless, but it can actually be quite useful. Since P(A|B)P(B) = P(B|A)P(A), if I know the relative likelihoods of me being Daniel Carrier and the universe ending next Tuesday, I can go from P(I am Daniel Carrier | The universe will end next Tuesday) to P(The universe will end next Tuesday | I am Daniel Carrier).